Abstract: Abstract. Generalizing work of Zagier, in an important recent paper Bruinier and Funke prove that the generating functions for traces of singular values of many modular functions are weight 3 2 modular forms. Using facts about half-integral weight modular forms, we obtain identities relating traces of singular moduli for modular functions of level p and 1. These follow from a general result relating coefficients of certain weakly holomorphic weight 3 2 modular forms of level 4p to Zagier’s traces of singular moduli.